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Let K be a finite complex, and let phi:C_p(K)->C_p(K) be a chain map, then sum_(p)(-1)^pTr(phi,C_p(K))=sum_(p)(-1)^pTr(phi_*,H_p(K)/T_p(K)).

A necessary and sufficient condition for a measure which is quasi-invariant under a transformation to be equivalent to an invariant probability measure is that the ...

The configuration formed by two curves starting at a point, called the vertex V, in a common direction. Horn angles are concrete illustrations of non-Archimedean geometries.

The inversion of a horn torus. If the inversion center lies on the torus, then the horn cyclide degenerates to a parabolic horn cyclide.

A hosohedron is a regular tiling or map on a sphere composed of p digons or spherical lunes, all with the same two vertices and the same vertex angles, 2pi/p. Its Schläfli ...

Let S be a set of n+1 symbols, then a Howell design H(s,2n) on symbol set S is an s×s array H such that 1. Every cell of H is either empty or contains an unordered pair of ...

The central point in a wheel graph W_n. The hub has degree n-1.

The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

100=10^2. Madachy (1979) gives a number of algebraic equations using the digits 1 to 9 which evaluate to 100, such as (7-5)^2+96+8-4-3-1 = 100 (1) 3^2+91+7+8-6-5-4 = 100 (2) ...

A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.